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Energy and Power

Let us consider an element in an electrical circuit through which a current I is flowing. Suppose there is a potential difference V across this element, and in a time $\Delta$t a charge $\Delta$Q passes by. The work $\Delta$W done by the electric field in moving this charge is given by, $\Delta$W = V$\Delta$Q . Thus, the work done per unit time, or the power P, is

P = $\displaystyle{\frac{\Delta W}{\Delta t}}$ = V$\displaystyle{\frac{\Delta Q}{\Delta t}}$ = VI. (5)

We recall the units of power are J/s, or Watts (W).

Electrical utilities normally bill on the basis of kilowatt-hours (kWh), which is the amount of energy the consumer has used in a given time period. One can convert kWh to J by the following formula:

1 kWh = 1000 Wh = 1000 $\displaystyle{\frac{{\:\rm J}\cdot\,{\:\rm h}}{{\:\rm s}}}$ = 1000 $\displaystyle{\frac{{\:\rm J}\cdot\,{\:\rm h}}{{\:\rm s}}}$ x 3600 = 3.6 x 106 J . (6)